The name of rogue waves first appeared in oceanography, where it referred to large spontaneous and unexpected water wave excitations that are a threat even to big ships [1]}, [2]}. Later, their counterparts in optics were also reported [3]}, [4]}. Due to their physical importance, rogue waves have received intensive theoretical and experimental studies in the past decade. On the theoretical front, analytical expressions of rogue waves have been derived in a wide variety of integrable physical models, such as the nonlinear Schrödinger (NLS) equation for wave-packet propagation in the ocean and optical systems [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, the derivative NLS equations for circularly polarized nonlinear Alfvén waves in plasmas and short-pulse propagation in a frequency-doubling crystal
[12]}, [13]}, [14]}, [15]}, [16]}, [17]}, the Manakov equations for light transmission in randomly birefringent fibers [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, and the three-wave resonant interaction equations [24]}, [25]}, [26]}, [27]}, [28]}, [29]}.
On the experimental front, various rogue wave solutions in the NLS equation and defocusing Manakov equations have been observed in water tanks and optical fibers [30]}, [31]}, [32]}, [33]}, [34]}. In these experiments, intimate knowledge of theoretical rogue wave solutions in the underlying nonlinear wave equations was utilized, which highlights the importance of theoretical developments on rogue waves for practical rogue wave verifications and predictions.
